Final answer:
The nurse should first remove the old patch when replacing a client's prescribed transdermal patch, followed by applying clean gloves.
Step-by-step explanation:
The nurse should first remove the old patch when replacing a client's prescribed transdermal patch. This is important to ensure that the client receives a fresh and effective dose of medication. After removing the old patch, the nurse should then apply clean gloves to maintain hygiene and prevent the spread of infection.